AN APPLICATION OF MERTON'S PORTFOLIO SELECTION PROBLEM TO THE CASE WITH A ZERO RECOVERY BOND

作者：Liang Yun^*

来源：International Journal of Innovative Computing Information and Control, 2011, 7(1): 141-149.

• Portfolio optimization
• Defaultable asset
• Risk management

In an earlier paper Liang [6], the author studied an optimization problem of consumption and investment strategy for an investor who can invest in a riskless asset and a no-zero recovery defaultable bond. In this paper, we demonstrate some results of the case with a zero recovery bond, and these are the theoretical basics of Liang [6].
Merton [7] was the first to formulate and solve such an optimization problem, and many researchers have extended and generalized the model of consumption and investment. However, optimization problems with defaultable assets have been rarely studied, though it is so important in today's financial market. This paper applies the framework of original Merton's model to a new market model that consists of a defaultable asset as well as a riskless asset. Under the assumption that the defaultable asset's price is modeled as a geometric Brownian motion with an unpredictable jump to zero, the optimal problem is reformulated and analytically solved.

• 出版日期2011-1